Artificial band gap

ABSTRACT

A method is disclosed for the induction of a suitable band gap and electron emissive properties into a substance, in which the substrate is provided with a surface structure corresponding to the interference of electron waves. Lithographic or similar techniques are used, either directly onto a metal mounted on the substrate, or onto a mold which then is used to impress the metal. In a preferred embodiment, a trench or series of nano-sized trenches are formed in the metal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a divisional application of application Ser. No. 09/634,615,filed Aug. 5, 2000, now U.S. Pat. No. 6,680,214, which claims thebenefit of U.S. Provisional Application No. 60/149,805, filed on Aug.18, 1999, and is a continuation application of application Ser. No.09/093,652, filed Jun. 8, 1998, now abandoned, and is related toapplication Ser. No. 09/020,654, filed Feb. 9, 1998, now U.S. Pat. No.6,281,514, all of which are herein incorporated by reference in theirentirety.

BACKGROUND OF THE INVENTION

The present invention is concerned with methods for fabricatingnanostructures to develop a band gap, and elementary particle emissionproperties.

Semiconductors, or semiconducting materials, have a small energy bandgap (about one eV or less) between the conduction band and the valenceband associated with the solid. This gap in energy distribution isuseful for microelectronics such as lasers, photodetectors, and tunneljunctions. Intrinsic semiconductors (not doped by another element)conduct due to the effect that raising the temperature will raise theenergy of some electrons to reach the conduction band. Intrinsicsemiconductors usually have a very low conductivity, due to thedifficulty of exciting an electron by approximately one eV.

Silicon is a commonly used semiconducting material and has limitedelectrical conductivity. In using silicon, designers of semiconductordevices are bound by the inherent material limitations of silicon.

The electrical conductivity of a semiconducting material is enhanced byadding small amounts of impurities, such as gallium arsenide. However,the process by which dopants are implanted in a semiconductor substrateof a semiconductor device is expensive and time-consuming. Also, thedesigning of semiconductor devices using doped materials currently knownin the art, such as silicon and gallium arsenide, often requires alengthy and expensive trial and error process to achieve the desiredband gap.

From the foregoing, it may be appreciated that a need has arisen for aband gap material that does not require doping, or materials havingother characteristics, to produce a desired band gap, and a method formaking such a band gap material.

It is well known in quantum mechanics that elementary particles havewave properties as well as corpuscular properties. The probability offinding an elementary particle at a given location is |ψ|² where ψ is acomplex wave function and has form of a de Broglie wave, as follows:ψ=A exp[(−i2π/h)(Et−pr)]  (1)

where h is Planck's constant; E is an energy of the particle; p is animpulse of the particle; r is a vector connecting initial and finallocations of the particle; and t is time.

There are well known fundamental relationships between the parameters ofthis probability wave and the energy and the impulse of the particle.

The wave number k related to the impulse of the particle as follows:p=(h/2π)k  (2)

The de Broglie wavelength, λ, is given by:λ=2π/k  (3)

At zero time, t=0, the space distribution of the probability wave may beobtained. Accordingly, substituting (2) into (1) gives:ψ=A exp(ikr)  (4)

FIG. 1 shows an elementary particle wave moving from left to rightperpendicular to a surface 104 dividing two domains. The surface isassociated with a potential barrier, which means the potential energy ofthe particle changes as it passes through it.

Incident wave 101 Aexp(ikx) moving towards the border will mainlyreflect back as reflected wave 103 βAexp(−ikx), and only a small partleaks through the surface to give transmitted wave 102 α(x)Aexp(ikx)(β≈1>>α). This is known as quantum mechanical tunneling. The elementaryparticle will pass the potential energy barrier with a low probability,depending on the potential energy barrier height.

Usagawa in U.S. Pat. No. 5,233,205 discloses a novel semiconductorsurface in which interaction between carriers such as electrons andholes in a mesoscopic region and the potential field in the mesoscopicregion leads to such effects as quantum interference and resonance, withthe result that output intensity may be changed. Shimizu in U.S. Pat.No. 5,521,735 discloses a novel wave combining and/or branching deviceand Aharanov-Bohm-type quantum interference devices which have no curvedwaveguide, but utilize double quantum well structures.

Mori in U.S. Pat. No. 5,247,223 discloses a quantum interferencesemiconductor device having a cathode, an anode and a gate mounted invacuum. Phase differences among the plurality of electron waves emittedfrom the cathode are controlled by the gate to give a quantuminterference device operating as an AB type transistor.

In U.S. patent application Ser. No. 09/020,654, filed Feb. 9, 1998,entitled “Method for Increasing Tunneling through a Potential Barrier”,Tavkhelidze teaches a method for promoting the passage of elementaryparticles at or through a potential barrier comprising providing apotential barrier having a geometrical shape for causing de Broglieinterference between said elementary particles.

Referring to FIG. 2, two domains are separated by a surface 201 havingan indented shape, with height a. An incident probability wave 202 isreflected from surface 201 to give two reflected waves. Wave 203 isreflected from top of the indent and wave 204 is reflected from thebottom of the indent. The reflected probability wave will thus be:

$\begin{matrix}{{{A\;{{\beta exp}\left( {- {ikx}} \right)}} + {A\;{{\beta exp}\left\lbrack {- {{ik}\left( {x + {2a}} \right)}} \right\rbrack}}} = {A\;{{{\beta exp}\left( {- {ikx}} \right)}\mspace{14mu}\left\lbrack {1 + {\exp\left( {- {ik2a}} \right)}} \right\rbrack}}} & (5)\end{matrix}$

When k2a=π+2πn, exp(−iπ)=−1 and equation (5) will equal zero.

Physically this means that for k2a=(2π/λ)2a=π+2πn and correspondinglya=λ(1+2n)/4, the reflected probability wave equals zero. Further thismeans that the particle will not reflect back from the border. Leakageof the probability wave through the barrier will occur with increasedprobability and will open many new possibilities for different practicalapplications.

Indents on the surface should have dimensions comparable to the deBroglie wavelength of an electron. In particular the indent heightshould be:a=nλ/2+λ/4  (6)

Here n=0, 1, 2, etc., and the indent width should be on the order of 2λ.If these requirements are satisfied, then elementary particles willaccumulate on the surface.

For semiconductor material, the velocities of electrons in an electroncloud is given by the Maxwell-Boltzman distribution:F(v)dv=n(m/2πK _(B) T) exp(−mv ²/2 K _(B) T)dv  (7)

where F(v) is the probability of an electron having a velocity between vand v+dv.

The average velocity of the electrons is:V _(av)=(3 K _(B) T/m)^(1/2)  (8)

and the de Broglie wavelength corresponding to this velocity, calculatedusing formulas (2), (3) and the classical approximation p=mv is:λ=h/(3m K _(B) T)^(1/2)=62 Å for T=300K.  (9)

This gives a value for a of 62/4=15.5 Å. Indents of this depth may beconstructed on a surface by a number of means known in the art ofmicro-machining. Alternatively, the indented shape may be introduced bydepositing a series of islands on the surface.

In metals, free electrons are strongly coupled to each other and form adegenerate electron cloud. Pauli's exclusion principle teaches that twoor more electrons may not occupy the same quantum mechanical state:their distribution is thus described by Fermi-Dirac rather thanMaxwell-Boltzman. In metals, free electrons occupy all the energy levelsfrom zero to the Fermi level (ε_(f))

Probability of occupation of energy states is almost constant in therange of 0–ε_(f) and has a value of unity. Only in the interval of a fewK_(B)T around ε_(f) does this probability drop from 1 to 0. In otherwords, there are no free states below ε_(f). This quantum phenomenonleads to the formal division of free electrons into two groups: Group 1,which comprises electrons having energies below the Fermi level, andGroup 2, comprising electrons with energies in the interval of fewK_(B)T around ε_(f).

For Group 1 electrons, all states having energies a little lower orhigher are already occupied, which means that it is quantum mechanicallyforbidden for them to take part in current transport. For the samereason electrons from Group 1 cannot interact with the lattice directlybecause it requires energy transfer between electron and lattice, whichis quantum mechanically forbidden.

Electrons from Group 2 have some empty energy states around them, andthey can both transport current and exchange energy with the lattice.Thus only electrons around the Fermi level are taken into account inmost cases when properties of metals are analyzed.

For electrons of Group 1, two observations may be made. The first isthat, if one aims to create a physical surface structure to achieveelectron wave interference, it is substantially easier to fabricate astructure for Group 1 electron wave interference, since their wavelengthof 50–100 Å corresponds to about 0.01ε_(f), (E˜k²˜(1/λ)²). Group 2electrons of single valence metals, on the other hand, where ε_(f)=2–3eV, have a de Broglie wavelength of around 5–10 Å, which is much smallerand more difficult to fabricate.

The second observation is that for quantum mechanical interferencebetween de Broglie waves to take place, the mean free path of theelectron should be large. Electrons from Group 1 satisfy thisrequirement because they effectively have an infinite mean free path dueto their very weak interaction with the lattice and impurities withinthe lattice.

If an electron from Group 1 has k₀=π/2a and energy ε₀, and is moving tothe indented surface 201. As discussed above, this particular electronwill not reflect back from the surface due to interference of de Brogliewaves, and will leave the metal in the case where the potential barrieris such type that allows electron tunneling (e.g. an electric field isapplied from outside the metal or there in another metal nearby).

Consider further that the metal is connected to a source of electrons,which provides electron 2, having energy close to ε_(f) (Group 2). Asrequired by the thermodynamic equilibrium, electron 2 will lose energyto occupy state ε₀, losing energy ε_(f)−ε₀, for example by emission of aphoton with energy ε_(p)=(ε_(f)−ε₀). If this is absorbed by electron 3,electron 3 will be excited to a state having energyε_(f)+ε_(p)=2ε_(f)−ε₀.

Thus as a consequence of the loss of electron 1, electron 3 from theFermi level is excited to a state having energy 2ε_(f)−ε₀, and could beemitted from the surface by thermionic emission or tunnel troughpotential barrier. The effective work function of electron 3 is reducedfrom the value of Φ to Φ−ε_(f)+ε₀=Φ−(ε_(f)−ε₀). In other words, the workfunction of electron 3 is reduced by ε_(f)−ε₀.

Thus indents on the surface of the metal not only allow electron 1 totunnel with high probability by interference of the de Broglie wave, butalso result in the enhanced probability of another electron emission(electron 3) by ordinary thermionic emission. The present inventiondeals with methods for constructing such a surface.

In the case that the potential barrier does not allow tunneling, theindented surface creates electron de Broglie wave interference insidethe metal, which leads to the creation of a special region below thefermi energy level. Inside that region, the number of possible quantumstates is dramatically decreased so that it could be regarded as anenergy gap.

Thus this approach has a two-fold benefit. Firstly, providing indents ona surface of a metal creates for that metal a band gap, and secondly,this approach will decrease the effective potential barrier betweenmetal and vacuum (the work function) in the case that the potentialbarrier is of such a type that an electron can tunnel through it.

This approach has many applications, including applications usuallyreserved for conventional semiconductors. Other applications includecathodes for vacuum tubes, thermionic converters, vacuum diode heatpumps, photoelectric converters, cold cathode sources, and many other inwhich electron emission from the surface is used.

In addition, an electron moving from vacuum into an anode electrodehaving an indented surface will also experience de Broglie interference,which will promote the movement of said electron into said electrode,thereby increasing the performance of the anode.

The development of low-cost, high-throughput techniques that can achieveresolutions of less than 50 nm is essential for the future manufacturingof semiconductor integrated circuits and the commercialization ofelectronic, opto-electronic, and magnetic nanodevices. Numeroustechnologies are under development. Scanning electron beam lithographyhas demonstrated 10 nm resolution; however, because it exposes point bypoint in a serial manner, the current throughput of the technique is toolow to be economically practical for mass production of sub-50 nmstructures. X-ray lithography has demonstrated 20 nm resolution in acontact printing mode and can have a high throughput, but its masktechnology and exposure systems are currently rather complex andexpensive. Lithographies based on scanning proximal probes, which haveshown a resolution of about 10 nm, are in the early stages ofdevelopment.

Conventional e-beam lithography involves exposing a thin layer of resist(usually a polymer film) coated on a metal film, itself deposited on asubstrate, to an electron beam. To create the desired pattern in theresist, the electron beam is scanned across the surface in apredetermined fashion. The chemical properties of the resist are changedby the influence of the electron beam, such that exposed areas may beremoved by a suitable solvent from the underlying metal film. Thesurface of the exposed metal film is etched, and finally unexposedresist is removed by another solvent.

In the etching process, the isotropic properties of the metal mean thatthe etchant will etch in both depth and in a direction parallel to thesubstrate surface under the resist. The depth of etching under theresist is approximately the same as the thickness of the metallic film.

If this approach is used to create two metal strip lines which are asnarrow as possible and separated by a minimum possible distance, thenthe under-etching means that the width of strip is decreased and thedistance between the strips is increased. In addition, part of theresist under-etched can collapse, which makes the edge of the stripirregular, or break during subsequent fabrication steps.

Overall, this means that the width of the strip is less than desired,and the distance between the strips is more than planned. Very thinstrips can be produced, but the minimum distance between strips isgreater than wanted. In another words, strips can be made which are evenless wide than the e-beam focusing dimension, but distance betweenstrips is greater than expected. In addition non-regularities on thestrip edges are obtained.

One approach to overcome the under-etch is focused ion beam (FIB)processing. This approach is described in U.S. Pat. No. 4,639,301 toDoherty et al., and uses an apparatus which makes possible the precisesputter etching and imaging of insulating and other targets, using afinely focused beam of ions. This apparatus produces and controls asubmicron beam of ions to precisely sputter etch the target. A beam ofelectrons directed on the target neutralizes the charge created by theincident ion beam. The FIB system can precisely deposit eitherinsulating or conducting materials onto an integrated circuit. However,this approach requires each item to be produced separately, andconsequently is slow and expensive.

Another approach to creating nano-structures is described by Chou etal., Science, Volume 272, Apr. 5, 1996, pages 85 to 87, entitled“Imprint Lithography with 25-nanometer Resolution.” Chou et al.demonstrate an alternative lithographic method, imprint lithography,that is based on compression molding and a pattern transfer process.Compression molding is a low-cost, high-throughput manufacturing thatprovides features with sizes of >1 μm which are routinely imprinted inplastics. Compact disks based on imprinting in poly-carbonate are oneexample. Other examples are imprinted polymethylmethacrylate (PMMA)structures with a feature size on the order of 10 μm and imprintedpolyester patterns with feature dimensions of several tens ofmicrometers. However, compression molding has not been developed into alithographic method to pattern semiconductors, metals, and othermaterials used in semiconductor integrated circuit manufacturing.

Chou's approach uses silicon dioxide molds on a silicon substrate. Themold was patterned with dots and lines having a minimum lateral featuresize of 25 nm by means of electron beam lithography, and the patternswere etched into the SiO₂ layer by fluorine-based RIE. This mold ispressed into a thin PMAA resist cast on a substrate, which creates athickness contrast pattern in the resist. After the mold is removed, ananisotropic etching process is used to transfer the pattern into theentire resist thickness by removing the remaining resist in thecompressed areas. This imprinted PMAA structure has structures with 25nm feature size and a high aspect ratio, smooth surfaces with aroughness of less than 3 nm and corners with nearly 90° angles. Thestructures, though of little use in nano-electronic devices, are usefulas masters in a lift off process for making nano-structures in metals: 5nm of Ti and 15 nm of Au are deposited onto the entire sample, and thenthe metal on the PMMA surface is removed as the PMMA is dissolved inacetone.

Chou's approach thus requires two stages to produce the finished metalstructure: first, nanoimprint lithography into a polymer mold; andsecond, a metal lift-off and reactive ion etch. The number of steps usedwill clearly bear on the difference between the original mold and thefinal product. In addition, the lift-off process destroys the polymermold, which means that a new PMAA mold must be produced in each processcycle.

BRIEF SUMMARY OF THE INVENTION

The present invention is a set of related methods for fabricatingnanostructures of required proportions in a material to give thatmaterial a desired band gap for emitting elementary particles. Therequired proportions substantially follow the following guidelines:Indents on the surface should have dimensions comparable to de Brogliewavelength of an electron. In particular, the indent or protrusion pitchis:a=nλ/2+λ/4  (6)

where n is an integer, such as 0, 1, 2, etc. and the width ofprotrusions or indentations should be of order of 2λ.

An object of the invention is to provide a method for creatingnanostructures of particular proportions in a material to develop inthat material a band gap, and elementary particle emission. A feature ofthe invention is that nanostructures are made on the surface of asubstrate by stamping a nano-structured mold or stamp into a softenedfilm of material, preferably metal, coated on a substrate. An advantageof the invention is that the complex and costly process of e-beamlithography is used only once for making the mold or stamp, which isused subsequently for the production of many hundreds of substrateshaving metal nano-structures on their surface.

Another advantage of the present invention is that the metalnanostructure may be produced from the nano-structured mold or stamp ina single step.

A further advantage of the present invention is that the dimensions ofthe structures created are limited only by the focusing possibilities ofthe electron beam or ion beam used to fabricate the mold.

An object of the present invention is to provide a method for removingexcess metal remaining on the substrate surface after the mold isremoved which leaves 90° angles in the nano-structure unchanged.

An advantage of the present invention is that removal of the thin layerof metal by means of bombardment with charged particles is easy tocontrol and it simultaneously cleans the surface.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

For a more complete explanation of the present, reference is made to thefollowing description and the accompanying drawings, in which:

FIG. 1 illustrates an incident probability wave, reflected probabilitywave and a transmitted probability wave.

FIG. 2 illustrates an incident probability wave, two reflectedprobability waves, and a transmitted probability wave interacting with asurface having a series of indents (or protrusions).

FIGS. 3( a)–(e) is a schematic representation of a process for using acharged particle beam and subsequent etching to make a nano-structuredsurface in a metal film coated on a substrate. The process may be usedto create a resultant surface, or to create a mold used for stampingsubsequent surfaces, of the required dimensions.

FIGS. 4( a)–(g) is a schematic representation of a process for using acharged particle beam to pattern the surface of a first materialdeposited onto a substrate, subsequent development, etching, anddeposition of a second material, to create islands of the secondmaterial on the surface of a substrate, according to the requireddimensions.

FIG. 5 shows how a mold, created by the method described with referenceto FIG. 1 (or with another, also viable structure or method as describedelsewhere in this patent), is used to imprint other, softened metals, tocreate in them the required surface structure for band gap and electronemission properties.

FIG. 6 illustrates an embodiment of the present invention having therequired shape for de Broglie interference, but having oxidized regionsto cause this interference, instead of a ridged surface.

FIG. 7 illustrates several different surface configurations, mostly3-dimensional, whilst the pattern of hexagons in FIG. 7( c) is a2-dimensional view depicting two heights of surface, in the shape ofhexagons.

DETAILED DESCRIPTION OF THE INVENTION

The invention is a method for constructing a surface to a material forincreasing de Broglie interference and thus creating a suitable band gapfor electron emission from the surface. A material's surface structureis formed in a configuration that provides a desired interferencepattern in the wave probability functions of an electron approaching thesurface. Alternatively, the invention may use elementary particles otherthan electrons. The desired interference pattern produces a suitableband gap for the surface, for electron emission.

The configuration of the surface may resemble a corrugated pattern ofsquared-off, “u”-shaped ridges and/or valleys. Alternatively, thepattern may be a regular pattern of rectangular “plateaus” or “holes,”where the pattern resembles a checkerboard. Further, one of ordinaryskill in the art will recognize that other configurations are possiblewhich may produce the desired interference of wave probabilityfunctions.

Materials useful for producing the above suitable surface structurescomprise those that, under stable conditions, will not form an oxidelayer, or will form an oxide layer of a known and reliable thickness. Inany case, the thickness of an oxide layer formed on the material shouldnot so obscure the relief of the surface that the conductive benefits ofthe geometrical shape of the surface are lost. Preferred materialsinclude, but are not restricted to, metals such as gold and chrome, andmaterials that under stable conditions form an oxide layer preferably ofless than about ten nanometers, and more preferably of less than aboutfive nanometers. In an embodiment of the invention, deliberate andfocused oxidation of sections of the surface creates the requiredpattern in the non-oxidized sections of the surface, causing thenecessary interference and bringing out the benefits of a suitable bandgap surface.

In an embodiment of the present invention, the surface is gold. Inalternative embodiments, other metals are used.

The required proportions for the surface are as follows: Indents on thesurface have dimensions comparable to the de Broglie wavelength of anelectron. In particular, indent or protrusion pitch should be:a=nλ/2+λ/4  (6)

where λ is the de Broglie wavelength for the electrons and n is aninteger, preferably having a value between 0 and 50 inclusive, (n=0, 1,2, . . . 50) and more preferably having a value between 0 and 16 (n=0,1, 1, . . . 16), and still more preferably having a value between 0 and4 (n=0, 1, 2, 3, 4).

Where the protrusions or indentations are of a trench-like shape runningacross the surface, their width should be of order of 2λ, and likewisethe distance between two adjacent protrusions or indentations. However,the shape is not always trench-like, as described later, having insteadregular or irregular shaped closed protrusions, or any other structurethat allows for wave interference. A preferred pitch-to-width ratio isapproximately 1:8. In some cases, this ratio may be as large as 1:10 oreven 1:15. The width may be as wide as about 10 nanometers, or as narrowas about 1 nanometer. The preferred pitch is the predicted best mode ofthe invention, however, because these sizes are incredibly tiny,experimentation will probably provide the most reasonable and effectivesizing.

FIG. 2 shows a surface configured to have a band gap and electronemission properties. The surface 201 comprises a series of paralleltrenches. Each trench has a cross-section resembling a “u” with squaredcorners. An incident probability wave 202 of an approaching electron isreflected from surface 201 to give reflected probability wave 203, andfrom the bottom of the indent to give reflected probability wave 204.Where the depth a of each trench is a solution to λ(1+2n)/4, where λ isthe de Broglie wavelength for the approaching electron, n is an integerpreferably having a value between 0 and 50 (n=0, 1, 2, . . . 50) andmore preferably having a value between 0 and 16 (n=0, 1, 2, . . . 16)and still more preferably having a value between 0 and 4 (n=0, 1, 2, 3,4), and the width of each trench is of order 2λ, the sum of reflectedprobability waves will equal zero. As a result, the probability wave 205will leak through the potential barrier of the surface with increasedprobability, thus increasing the probability of tunneling in the caseshape of potential barrier allows tunneling.

FIG. 3 depicts a method for creating nanostructures of proportions, asabove, onto a polymer resist, and then transferred onto a film,preferably metal, deposited on a substrate. This film is used as a mold,with which to stamp other metal films, or alternatively, as a materialused for its band gap and electron emission.

In FIG. 3( a), particle beam (ion beam or electron beam, for example)301 is focused to describe a pattern of predetermined shape and depth onthe face of a polymer resist, which has been formed onto a film ofmetal, which is deposited on a substrate. FIG. 3( b) shows a2-dimensional view of the modified molecules, which are developed by asuitable developing agent, to leave the remaining resist, as shown inFIG. 3( c). FIG. 3( d) shows how the resist and the metal film below itare then etched unidirectionally at a steady pace, to yield the resultsof the patterned metal film, as shown in FIG. 3( e).

This method creates a substance having a band gap and electron emission;however, this method may often be also used to create a mold, whichwould then be used to form an impression on subsequent surfaces. In anembodiment of the invention, suitable materials (such as a hard metal,with a high melting point, and which does not adhere to other metals)are used to create a mold, using methods described above. The mold isused, as shown in FIG. 5, to stamp other softened metals (attached tothe substrates), or to otherwise imprint them with the required pattern.The required surface is equally suitable as its topological opposite,both the mold and the resultant shape have band gap and electronemission properties.

FIG. 4 shows a method by which a charged particle beam patterns apolymer to a more variable depth, in which the metal is patterned to arequired depth by its deposition between islands to a required depth, orby subsequent etching until it is a required depth. FIG. 4( a) shows apolymer resist 403, mounted directly on a substrate 405, that ispatterned by a charged particle beam 401 to a suitable pattern but notnecessarily to the finally required depth. FIG. 4( b) shows the modifiedpolymer molecules 407, which are developed by a suitable developingagent. FIG. 4( c) shows the developed resist, having perhaps a thinlayer of resist remaining atop the substrate. Alternatively, the chargedparticle beam 401 can be aimed at the other areas of resist 403, insteadof as shown in FIG. 4( a), and then instead of FIG. 4( b), a developingagent which develops unmodified molecules could be utilized, to yieldthe same results as in FIG. 4( c), perhaps without the remaining thinlayer of resist 403 atop the substrate. In either event, the spacingbetween the remaining protrusions of resist 403 is of the order of 2λ,as described above.

FIG. 4( d) shows a thin layer of remaining resist in the indented areasthat may is removed by etching tool 411 that etches the whole polymerresist in a downward direction, until the thin layer disappears, asshown in FIG. 4( e). Only islands of resist remain. FIG. 4( f) showsmetal film 413 that then is unidirectionally deposited upon thesubstrate and atop the remaining islands of resist 403, to the requireddepth of the metal film, as described above. Alternatively, the metalfilm may be deposited too thickly, and then etched away to the requireddepth. FIG. 4( g) shows a remaining polymer resist (and deposited metalwhich formed above it) that has been removed with a “lift-off” orrelated technique, to leave just the islands of metal on the surface ofthe substrate, having the required depth and width. In relation to thesubstrate itself, these form a surface with an indented cross-section,having a band gap and electron emission.

FIG. 5 shows an embodiment in which a mold 514 having a surface, whichis the topological opposite of the nanostructure to be created, ispressed into a softened metal 515 coated on a substrate. The metal ishardened and the mold is removed.

FIG. 6 illustrates an embodiment of the invention. A metal film 609 ismounted on the substrate 605, and that is in the aim of an oxygen beam.The metal forms a stable oxide in the regions which are beamed 610, andthe resultant configuration between oxidized and non-oxidized regionscreates a surface structure capable of the required de Broglieinterference.

In another embodiment of the invention, the surface comprises a seriesof parallel ridges. Each ridge has a cross-section resembling a “mesa”or “plateau” with squared corners. The height a of each ridge and thewidth of each ridge correspond to the equations as above.

FIG. 7( a)–(d) demonstrate another embodiment of the invention. In FIG.7( a), the surface comprises a checkerboard-type arrangement of rows ofindividual rectangular-shaped “mesas” or “plateaus” and/or rows ofindividual rectangular-shaped “holes.” The height a of each “mesa”(and/or the depth of each “hole”) correspond to the equations as above.Alternatively, as in FIG. 7( b)–(d), 3-dimensional or 2-dimensionalviews of the upper surface, having appropriately scaled measurements,show a set of triangles, pentagons, hexagons, heptagons, octagons,circles, polygons, or combinations thereof. It is important that thesurface area of the top of the lower area and that of the top of thehigher area be identical, and it is preferable that they also form thesame shape as each other, as may be obtained for most but not all of theembodiments mentioned above.

The wave interference as described is to provide a metal or othermaterial with a band gap, and also, it encourages particle emission.Some materials, such as semiconductors, already contain one large orseveral smaller band gaps, and in one embodiment of the presentinvention, the modified surface does not create a band gap but increasesan already present band gap. Methods to form a desired band gap, or adesired level of particle emission, may include altering the precisionwith which the wave interference structure is created. Using therelationship to the de Broglie wavelength discussed above, aconfiguration of a desired material is determined that will produce thedesired band gap in the desired material. Finally, a surface of thematerial is formed to the determined configuration.

Thus, it is apparent that there has been provided, in accordance withthe invention, a method and apparatus for a band gap material thatsatisfies the advantages set forth above. Thus, the band gap material ofthe invention may be used in virtually all semiconductor materialapplications. Furthermore, the same method of providing a band gap in amaterial can be used to provide electron emission properties in thatsame material, since the two are related features, as has beendescribed.

The mold can be fabricated using techniques which allow anisotropicetching to achieve 90° angles. For example, it can be made from ananisotropic material, such as single crystal silicon, so that etching,for example anisotropic reactive ion etching, can take place only in thedirection normal to the surface. The mold is made from a material whichdoes not significantly adhere to the metal used in order to avoid damageto the metal film structure in the process of removing the mold.

Referring to FIG. 5( a), a mold 514 whose surface carries ananostructure which is the topological opposite of the nanostructurepattern to be fabricated, in that the mold 514 has protruding areaswhere indentations are desired in the final product, and carriesindentations where protrusions are required in the final product, ispressed into a softened metal film 515 coated on a substrate 505.

In another embodiment, the metal film is softened by heating. Thepressure used for imprinting and film temperature is adjusted forparticular metal used. In some embodiments, the metal of the finalsurface may be in liquid or even gas form, and solidify around the mold.

The substrate is preferably silicon, but may be any material which has amelting or softening temperature greater than that of the metal-coating.In an embodiment of the invention, gold is used, but any metal which hasa melting or softening temperature below that of the substrate materialmay be used. Some non-metals may also be used.

Metal film 515 is cooled and mold is removed to give the nano-structuredsurface.

Thus, the method for fabricating metal nano-structures on substratesurfaces described above, using a mold, is a low-cost, high-throughputtechnique especially as compared to using lithographic methods directlyonto the eventual surface, and yet it can achieve resolutions of lessthan 50 nm. The method is of great utility in the introduction orimprovement of a band gap to a material and in the construction ofsurfaces having enhanced electron emission.

The invention should not be construed as limited to the specificembodiments and methods described above but should be seen to includeequivalent embodiments and methods. For example, the substrate may beany material which has a melting or softening temperature greater thanthat of the metal-coating, and materials include silica, quartz, glass,diamond, and metal. Furthermore, the material used to coat the substrateis specified as being a metal, but it may be any substance which has amelting or softening temperature below that of the substrate material,including metals such as silver, nickel, and titanium, alloys,semiconductor materials, superconductor materials or polymers.

Structures have been described in detail but should not be construed asthe only possible configurations falling under the scope of the presentinvention. For example, in an embodiment, the shape of the surface isdescribed as having trenches running across its length. In a similarfashion, the trenches could run across the width of the surface. Theword ‘length’ has been used to denote a continuous trench. In a similarfashion, the trenches could run almost but not quite until the edges thesurface, or could indeed run the entire length of the surface. Asstated, the word ‘length’ has been used to denote a continuous trench,and not to limit the length to having to span the entire surface length.

A main focus of the invention is in having indents (or protrusions) of arequired depth, or pitch. The shape of the indents however is notspecified explicitly, because it could take on many forms and sizes allfalling within the scope of the invention. For example, instead of longtrenches, these could be checkerboard shape, with the black squares forexample, representing surface indentations, and white squares,protrusions. There could be hexagons, octagons or heptagons, or evencircles, imprinted into or protruding out of the surface.

It is preferable that the top surface area of the protruding regions ofthe surface be identical to the top surface area of the indentedregions. It is also preferable, but not crucial, that the shape of theprotruding regions be identical to the shape of the indented regions.Furthermore, it is preferable but by no means crucial that there shouldbe as few sharp corners in the side walls of the protrusions orindentations as possible. This minimizes the de Broglie diffraction. Forthis reason, a preferred geometry is long trenches, as opposed to thecheckerboard shape, however, the checkerboard shape also falls withinthe scope of the present invention. However, the structures describedare just a few embodiments of the present invention, which could haveregular indents, irregular, combinations of various shapes, etc. Therecould be a stepped surface, having more than one depth of indent, andthere could be more than one surface indented. The focus of thisspecification is on creating surface conditions for wave interference onthe tiny scale necessary for electrons and other elementary particles,and the invention should be construed in the light of the appendedclaims and their legal equivalents.

Indentations and protrusions to a basic surface are both described inthe specification, and there is really little technical differencebetween the two, except in their production method. Where an indentedsurface is referred to, it should be read as also referring to a surfacehaving protrusions, which, by definition, causes the surface to have anindented cross-section, having indents in the ‘spaces’ between theprotrusions.

While the specification refers to indentations, it is not intended tolimit the present invention to a plurality of indentations, indeed, asingle indented region will often be the configuration of choice.

The specification refers to modifying a single surface of a substrate,however, in some embodiments, more than one surface may have a patternedstructure, to cause interference.

In some cases the present invention may have to be used only in avacuum, to prevent surface decomposition, however in other cases, thismay not prove necessary, e.g. when the metal involved is known toproduce a stable and very thin oxide layer, then it may be usable evenwithout a vacuum, with the oxide layer not being substantiallydetrimental to wave interference.

Current lithographic techniques have been described in creation of themold, but other direct techniques are possible such as focused ion beamprocessing.

1. A method for the induction of a band gap in a substance, comprisingthe steps of: (a) mounting a material on a substrate, (b) forming atleast one nanostructure in said material by pressing a nanostructuredmold into said material, said nanostructure having a relief causing deBroglie interference of elementary particles.
 2. The method of claim 1in which said substrate is selected from the group consisting of:silica, quartz, glass, diamond, and metal.
 3. The method of claim 1 inwhich said material is selected from the group consisting of metals,alloys, superconductors, semiconductors, and polymers.
 4. The method ofclaim 1 further comprising the step of anisotropically milling theformed nanostructures with an ion beam until the substrate beneathindented areas in the nanostructures is exposed.
 5. The method of claim1 wherein said forming step further comprises the steps of: (a)softening said material prior to pressing into the material with ananostructured mold to imprint the structure in said material, and, (c)hardening the material, (d) separating the material from said mold. 6.The method of claim 5 wherein said softening step comprises heating thematerial.
 7. The method of claim 6, wherein said substrate is a metalselected from the group consisting of gold, silver, nickel, andtitanium.
 8. The method of claim 5 wherein said hardening step comprisescooling the material.
 9. The method of claim 1 wherein the moldcomprises at least one open-faced indented area, and at least oneprotruding area having the same cross-sectional area as thecross-sectional area of the indented area, and walls between saidindented and protruding areas being at a normal to both the indented andprotruding areas, said walls having a depth of λ(1+2n)/4, wherein λ isthe de Broglie wavelength of an incident electron, and n is an integer,and wherein said forming step comprises forming the relief of the moldin the material and allowing the release of any excess material in theprocess.
 10. The method of claim 7 in which said open-facedindentations, or said protrusions, or both, are selected from the groupconsisting of: triangles, pentagons, hexagons, octagons, heptagons,circles, and combinations thereof.